Smooth contours with grid lines
To connect the nodes smoothly, all that's needed is to (CtrlE > Edge Data) mark Freestyle edges on a low-poly version of your curved surface, as you appear to have done, and then assign a Subdivision Surface modifier with Catmull-Clark interpolation. (The newly generated faces and their sides are not visible to Freestyle, unless you apply the modifier, and mark them afterwards). Then you set the Freestyle Line Style to select only by Edge Mark. 

This is assuming that the result of CC subdivision is mathematically accurate enough for your purposes. If not, it is possible to select every n'th loop on a more densely divided grid. 


Select 2 parallel edges, n apart, on the loops you will eventually want to mark.
Hitting CtrlShiftNumpad + will select successive edges at the same interval, across the grid.
Using the Select menu in the header, select 'Loops' > 'Edge Loops'.


Loops will be selected at that interval, to be marked.